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Elasticity Theory (elasticity + theory)
Selected AbstractsA simplified analysis method for piled raft foundations in non-homogeneous soilsINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 2 2003Pastsakorn Kitiyodom Abstract A simplified method of numerical analysis based on elasticity theory has been developed for the analysis of axially and laterally loaded piled raft foundations embedded in non-homogeneous soils and incorporated into a computer program "PRAB". In this method, a hybrid model is employed in which the flexible raft is modelled as thin plates and the piles as elastic beams and the soil is treated as springs. The interactions between structural members, pile,soil,pile, pile,soil,raft and raft,soil,raft interactions, are approximated based on Mindlin's solutions for both vertical and lateral forces with consideration of non-homogeneous soils. The validity of the proposed method is verified through comparisons with some published solutions for single piles, pile groups and capped pile groups in non-homogeneous soils. Thereafter, the solutions from this approach for the analysis of axially and laterally loaded 4-pile pile groups and 4-pile piled rafts embedded in finite homogeneous and non-homogeneous soil layers are compared with those from three-dimensional finite element analysis. Good agreement between the present approach and the more rigorous finite element approach is demonstrated. Copyright © 2002 John Wiley & Sons, Ltd. [source] Three-dimensional vibration analysis of rectangular thick plates on Pasternak foundationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2004D. Zhou Abstract The free-vibration characteristics of rectangular thick plates resting on elastic foundations have been studied, based on the three-dimensional, linear and small strain elasticity theory. The foundation is described by the Pasternak (two-parameter) model. The Ritz method is used to derive the eigenvalue equation of the rectangular plate by augmenting the strain energy of the plate with the potential energy of the elastic foundation. The Chebyshev polynomials multiplied by a boundary function are selected as the admissible functions of the displacement functions in each direction. The approach is suitable for rectangular plates with arbitrary boundary conditions. Convergence and comparison studies have been performed on square plates on elastic foundations with different boundary conditions. It is shown that the present method has a rapid convergent rate, stable numerical operation and very high accuracy. Parametric investigations on the dynamic behaviour of clamped square thick plates on elastic foundations have been carried out in detail, with respect to different thickness,span ratios and foundation parameters. Some results found for the first time have been given and some important conclusions have been drawn. Copyright © 2004 John Wiley & Sons, Ltd. [source] Numerical evaluation of pressure from experimentally measured film thickness in EHL point contactLUBRICATION SCIENCE, Issue 1 2008Michal Vaverka Abstract This paper is concerned with elastohydrodynamic lubrication, especially the determination of lubricant film thickness and contact pressure within a point contact of friction surfaces of machine parts. A new solution technique for numerical determination of contact pressure is introduced. The direct measurement of contact pressure is very difficult. Hence, input data of lubricant film thickness obtained from the experiment based on colorimetric interferometry are used for the calculation of pressure using the inverse elasticity theory. The algorithm is enhanced by convolution in order to increase calculation speed. The approach described in this contribution gives reliable results on smooth contact and in the future, it will be extended to enable the study of contact of friction surfaces with asperities. Copyright © 2007 John Wiley & Sons, Ltd. [source] The Krein,von Neumann extension and its connection to an abstract buckling problemMATHEMATISCHE NACHRICHTEN, Issue 2 2010Mark S. Ashbaugh Abstract We prove the unitary equivalence of the inverse of the Krein,von Neumann extension (on the orthogonal complement of its kernel) of a densely defined, closed, strictly positive operator, S , ,IH for some , > 0 in a Hilbert space H to an abstract buckling problem operator. In the concrete case where in L2(,; dnx) for , , ,n an open, bounded (and sufficiently regular) domain, this recovers, as a particular case of a general result due to G. Grubb, that the eigenvalue problem for the Krein Laplacian SK (i.e., the Krein,von Neumann extension of S), SKv = ,v, , , 0, is in one-to-one correspondence with the problem of the buckling of a clamped plate, (-,)2u = , (-,)u in ,, , , 0, u , H02(,), where u and v are related via the pair of formulas u = SF -1 (-,)v, v = , -1(-,)u, with SF the Friedrichs extension of S. This establishes the Krein extension as a natural object in elasticity theory (in analogy to the Friedrichs extension, which found natural applications in quantum mechanics, elasticity, etc.) (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] | ||||||||||